<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified double Laplace transform method (MDLTM) is constructed for the proposed model. The MDLTM was used to obtain the analytic solution for the pseudo-hyperbolic telegraph equation of fractional order defined by the Caputo derivative. The proposed method is a highly effective analytical method for the fractional-order pseudo-hyperbolic telegraph equation. A test problem was presented as an example. Based on the results, it is clear that this method is more convenient and produces an analytic solution in fewer steps than other methods that require more steps to have an identical analytical solution. This paper claims to provide an analytic solution to the fractional order pseudohyperbolic telegraph equation order using the MDLTM. An analytical solution leads to an exact, closed-form solution that can be expressed in mathematical functions or known operations. Obtaining analytic solutions to PDEs is often challenging, especially for fractional order equations, making this achievement noteworthy.</p>
</abstract>

The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified double Laplace transform method (MDLTM) is constructed for the proposed model. The MDLTM was used to obtain the analytic solution for the pseudo-hyperbolic telegraph equation of fractional order defined by the Caputo derivative. The proposed method is a highly effective analytical method for the fractional-order pseudo-hyperbolic telegraph equation. A test problem was presented as an example. Based on the results, it is clear that this method is more convenient and produces an analytic solution in fewer steps than other methods that require more steps to have an identical analytical solution. This paper claims to provide an analytic solution to the fractional order pseudohyperbolic telegraph equation order using the MDLTM. An analytical solution leads to an exact, closed-form solution that can be expressed in mathematical functions or known operations. Obtaining analytic solutions to PDEs is often challenging, especially for fractional order equations, making this achievement noteworthy.

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

University of Duhok, College of Basic Education

Harran University, Faculty of Arts and Sciences

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified...

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Published Online: Jul 20, 2023

Page range: 105 - 114

Received: Apr 10, 2023

Accepted: Jun 01, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0008

Keywords
Pseudo-hyperbolic telegraph equation, caputo fractional derivative, modified double Laplace transform method, analytical solution

© 2023 Sadeq Taha Abdulazeez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Published Online: Jul 20, 2023

Page range: 105 - 114

Received: Apr 10, 2023

Accepted: Jun 01, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0008

KeywordsPseudo-hyperbolic telegraph equation, caputo fractional derivative, modified double Laplace transform method, analytical solution

© 2023 Sadeq Taha Abdulazeez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Pseudo-hyperbolic telegraph equation, caputo fractional derivative, modified double Laplace transform method, analytical solution